ISIL is designated under the UN Al Qaida sanctions regime (given effect by UN Security Council Resolution 1267) which is implemented in the EU by Council Regulation 881/2002, with the criminal penalties imposed in the UK by the Al Qaida (Asset Freezing) Regulations 2011. The Al Qaida financial sanctions is implemented in the UK by HM Treasury.
It is therefore a criminal offence for any legal or natural person, including financial institutions, to deal with funds belonging to ISIL or to make funds or economic resources available to ISIL. It is a criminal offence for individuals or organisations knowingly to provide support for ISIL, including by the facilitation of oil, oil products, or commodities including historic artefacts. This was most recently underlined in UN Security Council Resolution 2199, which the UK Government co-sponsored.